Explore BrainMass

Explore BrainMass

    Partitions on a Set

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    We denote the number of partitions of a set of n elements by P(n). Suppose the number of partitions of a set on n elements into k parts is denoted by P(n,k). Then obviously
    P(n) = P(n,1) + P(n,2) + ..... + P(n,n)

    Show that P(n,2) = 2^(n-1) - 1

    © BrainMass Inc. brainmass.com March 4, 2021, 6:01 pm ad1c9bdddf
    https://brainmass.com/math/combinatorics/partitions-set-24516

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    Proof:
    means the number ...

    Solution Summary

    Set partitions are investigated. The solution is detailed and well-presented.

    $2.49

    ADVERTISEMENT